Nuprl Lemma : callbyvalueall-single-append-nil
∀[F,a:Top]. (let x ⟵ [a] in let y ⟵ x @ [] in F[y] ~ let y ⟵ [a] in F[y])
Proof
Definitions occuring in Statement :
append: as @ bs,
cons: [a / b],
nil: [],
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
callbyvalueall: callbyvalueall,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
has-valueall: has-valueall(a),
implies: P ⇒ Q,
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
uiff: uiff(P;Q),
and: P ∧ Q,
has-value: (a)↓,
prop: ℙ
Lemmas referenced :
callbyvalueall-single,
has-valueall_wf_base,
evalall-sqequal,
has-valueall-single,
list_ind_nil_lemma,
list_ind_cons_lemma,
cbv_sqequal,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
voidElimination,
voidEquality,
baseApply,
closedConclusion,
baseClosed,
independent_isectElimination,
lambdaFormation,
dependent_functionElimination,
productElimination,
callbyvalueReduce
Latex:
\mforall{}[F,a:Top]. (let x \mleftarrow{}{} [a] in let y \mleftarrow{}{} x @ [] in F[y] \msim{} let y \mleftarrow{}{} [a] in F[y])
Date html generated:
2016_05_15-PM-02_08_45
Last ObjectModification:
2016_01_15-PM-10_21_43
Theory : untyped!computation
Home
Index